Victoria and Jane had a total of 48 beads. Jane gave ¹₃ of her beads to Victoria. In return, Victoria gave ¹₅ of the total number of beads that she had to Jane. In the end, each girl had the same number of beads. How many beads did Victoria have at first?

	Victoria	Jane	Total
Before 1	?	3 u	48
Change 1	+ 1 u	- 1 u
After 1	30	2 u	48
Before 2	5 p	2 u	48
Change 2	- 1 p	+ 1 p
After 2	4 p (24)	24	48

Since Jane gave some beads to Victoria and Victoria then gave some beads to Jane, it is an internal transfer of beads between the two girls. So, the total number of beads remains unchanged.

Number of beads that Jane and Victoria each had in the end is the same.

Number of beads that Victoria had in the end
= 48 ÷ 2
= 24

Number of beads that Victoria had in the end = 4 p

4 p = 24

1 p = 24 ÷ 4 = 6

Number of beads that Victoria had after receiving some beads from Jane
= 5 p
= 5 x 6
= 30

Number of beads that Jane had after giving to Victoria
= 48 - 30
= 18

2 u = 18

1 u = 18 ÷ 2 = 9

Number of beads that Jane had at first
= 3 u
= 3 x 9
= 27

Number of beads that Victoria had at first
= 48 - 27
= 21

Answer(s): 21